One of the successful aspects of Grand Theft Auto III is the mixture of types of impacts the player can have on the game.
You can have significant impact when you jump into a cop car, chase down perps, and run them off the road. When you simply steal cars and run people over, that's also impact (literally and figuratively).
But of course, there's no story involved with these sections of the game.
There are also elements of gameplay that have more limited impact. For instance, if you run missions for one gang, rival gang members will start shooting at you as a result of your reputation spreading. But it's a much lesser degree of impact, for no matter if it was you or if it was I who played the game, if we ran the same missions, the same rival gangs would fire upon us.